package algs.model.array;

/**
 * Funky alternative for selecting a pivot index by using the digits of PI.
 * 
 * @author George Heineman
 * @version 1.0, 6/15/08
 * @since 1.0
 */
public class PISelector implements IPivotIndex {
	
	/** current index. */
	private int idx;
	private int val = 0;
	private int len;
	private int base;
	
	/**
	 * Number of digits in a row that form the unique number. Must be small enough
	 * to be an actual integer value. 
	 * 
	 * @param numDigits    number of digits in a row for forming a unique number.
	 */
	public PISelector(int numDigits) {
		if (numDigits > 6) {
			throw new IllegalArgumentException ("PISelector only allows up to six digits to form number (" + numDigits + ")");
		}
		
		len = digits.length;
		base = 1;
		for (idx = 0; idx < numDigits; idx++) {
			val = val * 10 + digits[idx];
			base *= 10;
		}
		
		// one less than the number of digits to cycle through the values.
		base /= 10;
	}
	
	private void compute() {
		if (idx >= 9999) { idx = 0; }
		val = (val % base) * 10 + digits[idx++];
		if (idx >= len) { idx = 0; }
	}
	
	/** Return an index by using digits of PI. */
	public int selectPivotIndex(Comparable<?>[] ar, int left, int right) {
		int v = val;
		compute();  // get ready for next time.
		return left + v % (right - left + 1);
	}
	
	/** 9999 digits of pi. */
	private static int[] digits = new int[] {1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6,2,6,4,3,3,8,3,2,7,9,5,0,2,8,8,4,1,9,7,1,6,9,3,9,9,3,7,5,1,0,
		5,8,2,0,9,7,4,9,4,4,5,9,2,3,0,7,8,1,6,4,0,6,2,8,6,2,0,8,9,9,8,6,2,8,0,3,4,8,2,5,3,4,2,1,1,7,0,6,7,9,
		8,2,1,4,8,0,8,6,5,1,3,2,8,2,3,0,6,6,4,7,0,9,3,8,4,4,6,0,9,5,5,0,5,8,2,2,3,1,7,2,5,3,5,9,4,0,8,1,2,8,
		4,8,1,1,1,7,4,5,0,2,8,4,1,0,2,7,0,1,9,3,8,5,2,1,1,0,5,5,5,9,6,4,4,6,2,2,9,4,8,9,5,4,9,3,0,3,8,1,9,6,
		4,4,2,8,8,1,0,9,7,5,6,6,5,9,3,3,4,4,6,1,2,8,4,7,5,6,4,8,2,3,3,7,8,6,7,8,3,1,6,5,2,7,1,2,0,1,9,0,9,1,
		4,5,6,4,8,5,6,6,9,2,3,4,6,0,3,4,8,6,1,0,4,5,4,3,2,6,6,4,8,2,1,3,3,9,3,6,0,7,2,6,0,2,4,9,1,4,1,2,7,3,
		7,2,4,5,8,7,0,0,6,6,0,6,3,1,5,5,8,8,1,7,4,8,8,1,5,2,0,9,2,0,9,6,2,8,2,9,2,5,4,0,9,1,7,1,5,3,6,4,3,6,
		7,8,9,2,5,9,0,3,6,0,0,1,1,3,3,0,5,3,0,5,4,8,8,2,0,4,6,6,5,2,1,3,8,4,1,4,6,9,5,1,9,4,1,5,1,1,6,0,9,4,
		3,3,0,5,7,2,7,0,3,6,5,7,5,9,5,9,1,9,5,3,0,9,2,1,8,6,1,1,7,3,8,1,9,3,2,6,1,1,7,9,3,1,0,5,1,1,8,5,4,8,
		0,7,4,4,6,2,3,7,9,9,6,2,7,4,9,5,6,7,3,5,1,8,8,5,7,5,2,7,2,4,8,9,1,2,2,7,9,3,8,1,8,3,0,1,1,9,4,9,1,2,
		9,8,3,3,6,7,3,3,6,2,4,4,0,6,5,6,6,4,3,0,8,6,0,2,1,3,9,4,9,4,6,3,9,5,2,2,4,7,3,7,1,9,0,7,0,2,1,7,9,8,
		6,0,9,4,3,7,0,2,7,7,0,5,3,9,2,1,7,1,7,6,2,9,3,1,7,6,7,5,2,3,8,4,6,7,4,8,1,8,4,6,7,6,6,9,4,0,5,1,3,2,
		0,0,0,5,6,8,1,2,7,1,4,5,2,6,3,5,6,0,8,2,7,7,8,5,7,7,1,3,4,2,7,5,7,7,8,9,6,0,9,1,7,3,6,3,7,1,7,8,7,2,
		1,4,6,8,4,4,0,9,0,1,2,2,4,9,5,3,4,3,0,1,4,6,5,4,9,5,8,5,3,7,1,0,5,0,7,9,2,2,7,9,6,8,9,2,5,8,9,2,3,5,
		4,2,0,1,9,9,5,6,1,1,2,1,2,9,0,2,1,9,6,0,8,6,4,0,3,4,4,1,8,1,5,9,8,1,3,6,2,9,7,7,4,7,7,1,3,0,9,9,6,0,
		5,1,8,7,0,7,2,1,1,3,4,9,9,9,9,9,9,8,3,7,2,9,7,8,0,4,9,9,5,1,0,5,9,7,3,1,7,3,2,8,1,6,0,9,6,3,1,8,5,9,
		5,0,2,4,4,5,9,4,5,5,3,4,6,9,0,8,3,0,2,6,4,2,5,2,2,3,0,8,2,5,3,3,4,4,6,8,5,0,3,5,2,6,1,9,3,1,1,8,8,1,
		7,1,0,1,0,0,0,3,1,3,7,8,3,8,7,5,2,8,8,6,5,8,7,5,3,3,2,0,8,3,8,1,4,2,0,6,1,7,1,7,7,6,6,9,1,4,7,3,0,3,
		5,9,8,2,5,3,4,9,0,4,2,8,7,5,5,4,6,8,7,3,1,1,5,9,5,6,2,8,6,3,8,8,2,3,5,3,7,8,7,5,9,3,7,5,1,9,5,7,7,8,
		1,8,5,7,7,8,0,5,3,2,1,7,1,2,2,6,8,0,6,6,1,3,0,0,1,9,2,7,8,7,6,6,1,1,1,9,5,9,0,9,2,1,6,4,2,0,1,9,8,9,
		3,8,0,9,5,2,5,7,2,0,1,0,6,5,4,8,5,8,6,3,2,7,8,8,6,5,9,3,6,1,5,3,3,8,1,8,2,7,9,6,8,2,3,0,3,0,1,9,5,2,
		0,3,5,3,0,1,8,5,2,9,6,8,9,9,5,7,7,3,6,2,2,5,9,9,4,1,3,8,9,1,2,4,9,7,2,1,7,7,5,2,8,3,4,7,9,1,3,1,5,1,
		5,5,7,4,8,5,7,2,4,2,4,5,4,1,5,0,6,9,5,9,5,0,8,2,9,5,3,3,1,1,6,8,6,1,7,2,7,8,5,5,8,8,9,0,7,5,0,9,8,3,
		8,1,7,5,4,6,3,7,4,6,4,9,3,9,3,1,9,2,5,5,0,6,0,4,0,0,9,2,7,7,0,1,6,7,1,1,3,9,0,0,9,8,4,8,8,2,4,0,1,2,
		8,5,8,3,6,1,6,0,3,5,6,3,7,0,7,6,6,0,1,0,4,7,1,0,1,8,1,9,4,2,9,5,5,5,9,6,1,9,8,9,4,6,7,6,7,8,3,7,4,4,
		9,4,4,8,2,5,5,3,7,9,7,7,4,7,2,6,8,4,7,1,0,4,0,4,7,5,3,4,6,4,6,2,0,8,0,4,6,6,8,4,2,5,9,0,6,9,4,9,1,2,
		9,3,3,1,3,6,7,7,0,2,8,9,8,9,1,5,2,1,0,4,7,5,2,1,6,2,0,5,6,9,6,6,0,2,4,0,5,8,0,3,8,1,5,0,1,9,3,5,1,1,
		2,5,3,3,8,2,4,3,0,0,3,5,5,8,7,6,4,0,2,4,7,4,9,6,4,7,3,2,6,3,9,1,4,1,9,9,2,7,2,6,0,4,2,6,9,9,2,2,7,9,
		6,7,8,2,3,5,4,7,8,1,6,3,6,0,0,9,3,4,1,7,2,1,6,4,1,2,1,9,9,2,4,5,8,6,3,1,5,0,3,0,2,8,6,1,8,2,9,7,4,5,
		5,5,7,0,6,7,4,9,8,3,8,5,0,5,4,9,4,5,8,8,5,8,6,9,2,6,9,9,5,6,9,0,9,2,7,2,1,0,7,9,7,5,0,9,3,0,2,9,5,5,
		3,2,1,1,6,5,3,4,4,9,8,7,2,0,2,7,5,5,9,6,0,2,3,6,4,8,0,6,6,5,4,9,9,1,1,9,8,8,1,8,3,4,7,9,7,7,5,3,5,6,
		6,3,6,9,8,0,7,4,2,6,5,4,2,5,2,7,8,6,2,5,5,1,8,1,8,4,1,7,5,7,4,6,7,2,8,9,0,9,7,7,7,7,2,7,9,3,8,0,0,0,
		8,1,6,4,7,0,6,0,0,1,6,1,4,5,2,4,9,1,9,2,1,7,3,2,1,7,2,1,4,7,7,2,3,5,0,1,4,1,4,4,1,9,7,3,5,6,8,5,4,8,
		1,6,1,3,6,1,1,5,7,3,5,2,5,5,2,1,3,3,4,7,5,7,4,1,8,4,9,4,6,8,4,3,8,5,2,3,3,2,3,9,0,7,3,9,4,1,4,3,3,3,
		4,5,4,7,7,6,2,4,1,6,8,6,2,5,1,8,9,8,3,5,6,9,4,8,5,5,6,2,0,9,9,2,1,9,2,2,2,1,8,4,2,7,2,5,5,0,2,5,4,2,
		5,6,8,8,7,6,7,1,7,9,0,4,9,4,6,0,1,6,5,3,4,6,6,8,0,4,9,8,8,6,2,7,2,3,2,7,9,1,7,8,6,0,8,5,7,8,4,3,8,3,
		8,2,7,9,6,7,9,7,6,6,8,1,4,5,4,1,0,0,9,5,3,8,8,3,7,8,6,3,6,0,9,5,0,6,8,0,0,6,4,2,2,5,1,2,5,2,0,5,1,1,
		7,3,9,2,9,8,4,8,9,6,0,8,4,1,2,8,4,8,8,6,2,6,9,4,5,6,0,4,2,4,1,9,6,5,2,8,5,0,2,2,2,1,0,6,6,1,1,8,6,3,
		0,6,7,4,4,2,7,8,6,2,2,0,3,9,1,9,4,9,4,5,0,4,7,1,2,3,7,1,3,7,8,6,9,6,0,9,5,6,3,6,4,3,7,1,9,1,7,2,8,7,
		4,6,7,7,6,4,6,5,7,5,7,3,9,6,2,4,1,3,8,9,0,8,6,5,8,3,2,6,4,5,9,9,5,8,1,3,3,9,0,4,7,8,0,2,7,5,9,0,0,9,
		9,4,6,5,7,6,4,0,7,8,9,5,1,2,6,9,4,6,8,3,9,8,3,5,2,5,9,5,7,0,9,8,2,5,8,2,2,6,2,0,5,2,2,4,8,9,4,0,7,7,
		2,6,7,1,9,4,7,8,2,6,8,4,8,2,6,0,1,4,7,6,9,9,0,9,0,2,6,4,0,1,3,6,3,9,4,4,3,7,4,5,5,3,0,5,0,6,8,2,0,3,
		4,9,6,2,5,2,4,5,1,7,4,9,3,9,9,6,5,1,4,3,1,4,2,9,8,0,9,1,9,0,6,5,9,2,5,0,9,3,7,2,2,1,6,9,6,4,6,1,5,1,
		5,7,0,9,8,5,8,3,8,7,4,1,0,5,9,7,8,8,5,9,5,9,7,7,2,9,7,5,4,9,8,9,3,0,1,6,1,7,5,3,9,2,8,4,6,8,1,3,8,2,
		6,8,6,8,3,8,6,8,9,4,2,7,7,4,1,5,5,9,9,1,8,5,5,9,2,5,2,4,5,9,5,3,9,5,9,4,3,1,0,4,9,9,7,2,5,2,4,6,8,0,
		8,4,5,9,8,7,2,7,3,6,4,4,6,9,5,8,4,8,6,5,3,8,3,6,7,3,6,2,2,2,6,2,6,0,9,9,1,2,4,6,0,8,0,5,1,2,4,3,8,8,
		4,3,9,0,4,5,1,2,4,4,1,3,6,5,4,9,7,6,2,7,8,0,7,9,7,7,1,5,6,9,1,4,3,5,9,9,7,7,0,0,1,2,9,6,1,6,0,8,9,4,
		4,1,6,9,4,8,6,8,5,5,5,8,4,8,4,0,6,3,5,3,4,2,2,0,7,2,2,2,5,8,2,8,4,8,8,6,4,8,1,5,8,4,5,6,0,2,8,5,0,6,
		0,1,6,8,4,2,7,3,9,4,5,2,2,6,7,4,6,7,6,7,8,8,9,5,2,5,2,1,3,8,5,2,2,5,4,9,9,5,4,6,6,6,7,2,7,8,2,3,9,8,
		6,4,5,6,5,9,6,1,1,6,3,5,4,8,8,6,2,3,0,5,7,7,4,5,6,4,9,8,0,3,5,5,9,3,6,3,4,5,6,8,1,7,4,3,2,4,1,1,2,5,
		1,5,0,7,6,0,6,9,4,7,9,4,5,1,0,9,6,5,9,6,0,9,4,0,2,5,2,2,8,8,7,9,7,1,0,8,9,3,1,4,5,6,6,9,1,3,6,8,6,7,
		2,2,8,7,4,8,9,4,0,5,6,0,1,0,1,5,0,3,3,0,8,6,1,7,9,2,8,6,8,0,9,2,0,8,7,4,7,6,0,9,1,7,8,2,4,9,3,8,5,8,
		9,0,0,9,7,1,4,9,0,9,6,7,5,9,8,5,2,6,1,3,6,5,5,4,9,7,8,1,8,9,3,1,2,9,7,8,4,8,2,1,6,8,2,9,9,8,9,4,8,7,
		2,2,6,5,8,8,0,4,8,5,7,5,6,4,0,1,4,2,7,0,4,7,7,5,5,5,1,3,2,3,7,9,6,4,1,4,5,1,5,2,3,7,4,6,2,3,4,3,6,4,
		5,4,2,8,5,8,4,4,4,7,9,5,2,6,5,8,6,7,8,2,1,0,5,1,1,4,1,3,5,4,7,3,5,7,3,9,5,2,3,1,1,3,4,2,7,1,6,6,1,0,
		2,1,3,5,9,6,9,5,3,6,2,3,1,4,4,2,9,5,2,4,8,4,9,3,7,1,8,7,1,1,0,1,4,5,7,6,5,4,0,3,5,9,0,2,7,9,9,3,4,4,
		0,3,7,4,2,0,0,7,3,1,0,5,7,8,5,3,9,0,6,2,1,9,8,3,8,7,4,4,7,8,0,8,4,7,8,4,8,9,6,8,3,3,2,1,4,4,5,7,1,3,
		8,6,8,7,5,1,9,4,3,5,0,6,4,3,0,2,1,8,4,5,3,1,9,1,0,4,8,4,8,1,0,0,5,3,7,0,6,1,4,6,8,0,6,7,4,9,1,9,2,7,
		8,1,9,1,1,9,7,9,3,9,9,5,2,0,6,1,4,1,9,6,6,3,4,2,8,7,5,4,4,4,0,6,4,3,7,4,5,1,2,3,7,1,8,1,9,2,1,7,9,9,
		9,8,3,9,1,0,1,5,9,1,9,5,6,1,8,1,4,6,7,5,1,4,2,6,9,1,2,3,9,7,4,8,9,4,0,9,0,7,1,8,6,4,9,4,2,3,1,9,6,1,
		5,6,7,9,4,5,2,0,8,0,9,5,1,4,6,5,5,0,2,2,5,2,3,1,6,0,3,8,8,1,9,3,0,1,4,2,0,9,3,7,6,2,1,3,7,8,5,5,9,5,
		6,6,3,8,9,3,7,7,8,7,0,8,3,0,3,9,0,6,9,7,9,2,0,7,7,3,4,6,7,2,2,1,8,2,5,6,2,5,9,9,6,6,1,5,0,1,4,2,1,5,
		0,3,0,6,8,0,3,8,4,4,7,7,3,4,5,4,9,2,0,2,6,0,5,4,1,4,6,6,5,9,2,5,2,0,1,4,9,7,4,4,2,8,5,0,7,3,2,5,1,8,
		6,6,6,0,0,2,1,3,2,4,3,4,0,8,8,1,9,0,7,1,0,4,8,6,3,3,1,7,3,4,6,4,9,6,5,1,4,5,3,9,0,5,7,9,6,2,6,8,5,6,
		1,0,0,5,5,0,8,1,0,6,6,5,8,7,9,6,9,9,8,1,6,3,5,7,4,7,3,6,3,8,4,0,5,2,5,7,1,4,5,9,1,0,2,8,9,7,0,6,4,1,
		4,0,1,1,0,9,7,1,2,0,6,2,8,0,4,3,9,0,3,9,7,5,9,5,1,5,6,7,7,1,5,7,7,0,0,4,2,0,3,3,7,8,6,9,9,3,6,0,0,7,
		2,3,0,5,5,8,7,6,3,1,7,6,3,5,9,4,2,1,8,7,3,1,2,5,1,4,7,1,2,0,5,3,2,9,2,8,1,9,1,8,2,6,1,8,6,1,2,5,8,6,
		7,3,2,1,5,7,9,1,9,8,4,1,4,8,4,8,8,2,9,1,6,4,4,7,0,6,0,9,5,7,5,2,7,0,6,9,5,7,2,2,0,9,1,7,5,6,7,1,1,6,
		7,2,2,9,1,0,9,8,1,6,9,0,9,1,5,2,8,0,1,7,3,5,0,6,7,1,2,7,4,8,5,8,3,2,2,2,8,7,1,8,3,5,2,0,9,3,5,3,9,6,
		5,7,2,5,1,2,1,0,8,3,5,7,9,1,5,1,3,6,9,8,8,2,0,9,1,4,4,4,2,1,0,0,6,7,5,1,0,3,3,4,6,7,1,1,0,3,1,4,1,2,
		6,7,1,1,1,3,6,9,9,0,8,6,5,8,5,1,6,3,9,8,3,1,5,0,1,9,7,0,1,6,5,1,5,1,1,6,8,5,1,7,1,4,3,7,6,5,7,6,1,8,
		3,5,1,5,5,6,5,0,8,8,4,9,0,9,9,8,9,8,5,9,9,8,2,3,8,7,3,4,5,5,2,8,3,3,1,6,3,5,5,0,7,6,4,7,9,1,8,5,3,5,
		8,9,3,2,2,6,1,8,5,4,8,9,6,3,2,1,3,2,9,3,3,0,8,9,8,5,7,0,6,4,2,0,4,6,7,5,2,5,9,0,7,0,9,1,5,4,8,1,4,1,
		6,5,4,9,8,5,9,4,6,1,6,3,7,1,8,0,2,7,0,9,8,1,9,9,4,3,0,9,9,2,4,4,8,8,9,5,7,5,7,1,2,8,2,8,9,0,5,9,2,3,
		2,3,3,2,6,0,9,7,2,9,9,7,1,2,0,8,4,4,3,3,5,7,3,2,6,5,4,8,9,3,8,2,3,9,1,1,9,3,2,5,9,7,4,6,3,6,6,7,3,0,
		5,8,3,6,0,4,1,4,2,8,1,3,8,8,3,0,3,2,0,3,8,2,4,9,0,3,7,5,8,9,8,5,2,4,3,7,4,4,1,7,0,2,9,1,3,2,7,6,5,6,
		1,8,0,9,3,7,7,3,4,4,4,0,3,0,7,0,7,4,6,9,2,1,1,2,0,1,9,1,3,0,2,0,3,3,0,3,8,0,1,9,7,6,2,1,1,0,1,1,0,0,
		4,4,9,2,9,3,2,1,5,1,6,0,8,4,2,4,4,4,8,5,9,6,3,7,6,6,9,8,3,8,9,5,2,2,8,6,8,4,7,8,3,1,2,3,5,5,2,6,5,8,
		2,1,3,1,4,4,9,5,7,6,8,5,7,2,6,2,4,3,3,4,4,1,8,9,3,0,3,9,6,8,6,4,2,6,2,4,3,4,1,0,7,7,3,2,2,6,9,7,8,0,
		2,8,0,7,3,1,8,9,1,5,4,4,1,1,0,1,0,4,4,6,8,2,3,2,5,2,7,1,6,2,0,1,0,5,2,6,5,2,2,7,2,1,1,1,6,6,0,3,9,6,
		6,6,5,5,7,3,0,9,2,5,4,7,1,1,0,5,5,7,8,5,3,7,6,3,4,6,6,8,2,0,6,5,3,1,0,9,8,9,6,5,2,6,9,1,8,6,2,0,5,6,
		4,7,6,9,3,1,2,5,7,0,5,8,6,3,5,6,6,2,0,1,8,5,5,8,1,0,0,7,2,9,3,6,0,6,5,9,8,7,6,4,8,6,1,1,7,9,1,0,4,5,
		3,3,4,8,8,5,0,3,4,6,1,1,3,6,5,7,6,8,6,7,5,3,2,4,9,4,4,1,6,6,8,0,3,9,6,2,6,5,7,9,7,8,7,7,1,8,5,5,6,0,
		8,4,5,5,2,9,6,5,4,1,2,6,6,5,4,0,8,5,3,0,6,1,4,3,4,4,4,3,1,8,5,8,6,7,6,9,7,5,1,4,5,6,6,1,4,0,6,8,0,0,
		7,0,0,2,3,7,8,7,7,6,5,9,1,3,4,4,0,1,7,1,2,7,4,9,4,7,0,4,2,0,5,6,2,2,3,0,5,3,8,9,9,4,5,6,1,3,1,4,0,7,
		1,1,2,7,0,0,0,4,0,7,8,5,4,7,3,3,2,6,9,9,3,9,0,8,1,4,5,4,6,6,4,6,4,5,8,8,0,7,9,7,2,7,0,8,2,6,6,8,3,0,
		6,3,4,3,2,8,5,8,7,8,5,6,9,8,3,0,5,2,3,5,8,0,8,9,3,3,0,6,5,7,5,7,4,0,6,7,9,5,4,5,7,1,6,3,7,7,5,2,5,4,
		2,0,2,1,1,4,9,5,5,7,6,1,5,8,1,4,0,0,2,5,0,1,2,6,2,2,8,5,9,4,1,3,0,2,1,6,4,7,1,5,5,0,9,7,9,2,5,9,2,3,
		0,9,9,0,7,9,6,5,4,7,3,7,6,1,2,5,5,1,7,6,5,6,7,5,1,3,5,7,5,1,7,8,2,9,6,6,6,4,5,4,7,7,9,1,7,4,5,0,1,1,
		2,9,9,6,1,4,8,9,0,3,0,4,6,3,9,9,4,7,1,3,2,9,6,2,1,0,7,3,4,0,4,3,7,5,1,8,9,5,7,3,5,9,6,1,4,5,8,9,0,1,
		9,3,8,9,7,1,3,1,1,1,7,9,0,4,2,9,7,8,2,8,5,6,4,7,5,0,3,2,0,3,1,9,8,6,9,1,5,1,4,0,2,8,7,0,8,0,8,5,9,9,
		0,4,8,0,1,0,9,4,1,2,1,4,7,2,2,1,3,1,7,9,4,7,6,4,7,7,7,2,6,2,2,4,1,4,2,5,4,8,5,4,5,4,0,3,3,2,1,5,7,1,
		8,5,3,0,6,1,4,2,2,8,8,1,3,7,5,8,5,0,4,3,0,6,3,3,2,1,7,5,1,8,2,9,7,9,8,6,6,2,2,3,7,1,7,2,1,5,9,1,6,0,
		7,7,1,6,6,9,2,5,4,7,4,8,7,3,8,9,8,6,6,5,4,9,4,9,4,5,0,1,1,4,6,5,4,0,6,2,8,4,3,3,6,6,3,9,3,7,9,0,0,3,
		9,7,6,9,2,6,5,6,7,2,1,4,6,3,8,5,3,0,6,7,3,6,0,9,6,5,7,1,2,0,9,1,8,0,7,6,3,8,3,2,7,1,6,6,4,1,6,2,7,4,
		8,8,8,8,0,0,7,8,6,9,2,5,6,0,2,9,0,2,2,8,4,7,2,1,0,4,0,3,1,7,2,1,1,8,6,0,8,2,0,4,1,9,0,0,0,4,2,2,9,6,
		6,1,7,1,1,9,6,3,7,7,9,2,1,3,3,7,5,7,5,1,1,4,9,5,9,5,0,1,5,6,6,0,4,9,6,3,1,8,6,2,9,4,7,2,6,5,4,7,3,6,
		4,2,5,2,3,0,8,1,7,7,0,3,6,7,5,1,5,9,0,6,7,3,5,0,2,3,5,0,7,2,8,3,5,4,0,5,6,7,0,4,0,3,8,6,7,4,3,5,1,3,
		6,2,2,2,2,4,7,7,1,5,8,9,1,5,0,4,9,5,3,0,9,8,4,4,4,8,9,3,3,3,0,9,6,3,4,0,8,7,8,0,7,6,9,3,2,5,9,9,3,9,
		7,8,0,5,4,1,9,3,4,1,4,4,7,3,7,7,4,4,1,8,4,2,6,3,1,2,9,8,6,0,8,0,9,9,8,8,8,6,8,7,4,1,3,2,6,0,4,7,2,1,
		5,6,9,5,1,6,2,3,9,6,5,8,6,4,5,7,3,0,2,1,6,3,1,5,9,8,1,9,3,1,9,5,1,6,7,3,5,3,8,1,2,9,7,4,1,6,7,7,2,9,
		4,7,8,6,7,2,4,2,2,9,2,4,6,5,4,3,6,6,8,0,0,9,8,0,6,7,6,9,2,8,2,3,8,2,8,0,6,8,9,9,6,4,0,0,4,8,2,4,3,5,
		4,0,3,7,0,1,4,1,6,3,1,4,9,6,5,8,9,7,9,4,0,9,2,4,3,2,3,7,8,9,6,9,0,7,0,6,9,7,7,9,4,2,2,3,6,2,5,0,8,2,
		2,1,6,8,8,9,5,7,3,8,3,7,9,8,6,2,3,0,0,1,5,9,3,7,7,6,4,7,1,6,5,1,2,2,8,9,3,5,7,8,6,0,1,5,8,8,1,6,1,7,
		5,5,7,8,2,9,7,3,5,2,3,3,4,4,6,0,4,2,8,1,5,1,2,6,2,7,2,0,3,7,3,4,3,1,4,6,5,3,1,9,7,7,7,7,4,1,6,0,3,1,
		9,9,0,6,6,5,5,4,1,8,7,6,3,9,7,9,2,9,3,3,4,4,1,9,5,2,1,5,4,1,3,4,1,8,9,9,4,8,5,4,4,4,7,3,4,5,6,7,3,8,
		3,1,6,2,4,9,9,3,4,1,9,1,3,1,8,1,4,8,0,9,2,7,7,7,7,1,0,3,8,6,3,8,7,7,3,4,3,1,7,7,2,0,7,5,4,5,6,5,4,5,
		3,2,2,0,7,7,7,0,9,2,1,2,0,1,9,0,5,1,6,6,0,9,6,2,8,0,4,9,0,9,2,6,3,6,0,1,9,7,5,9,8,8,2,8,1,6,1,3,3,2,
		3,1,6,6,6,3,6,5,2,8,6,1,9,3,2,6,6,8,6,3,3,6,0,6,2,7,3,5,6,7,6,3,0,3,5,4,4,7,7,6,2,8,0,3,5,0,4,5,0,7,
		7,7,2,3,5,5,4,7,1,0,5,8,5,9,5,4,8,7,0,2,7,9,0,8,1,4,3,5,6,2,4,0,1,4,5,1,7,1,8,0,6,2,4,6,4,3,6,2,6,7,
		9,4,5,6,1,2,7,5,3,1,8,1,3,4,0,7,8,3,3,0,3,3,6,2,5,4,2,3,2,7,8,3,9,4,4,9,7,5,3,8,2,4,3,7,2,0,5,8,3,5,
		3,1,1,4,7,7,1,1,9,9,2,6,0,6,3,8,1,3,3,4,6,7,7,6,8,7,9,6,9,5,9,7,0,3,0,9,8,3,3,9,1,3,0,7,7,1,0,9,8,7,
		0,4,0,8,5,9,1,3,3,7,4,6,4,1,4,4,2,8,2,2,7,7,2,6,3,4,6,5,9,4,7,0,4,7,4,5,8,7,8,4,7,7,8,7,2,0,1,9,2,7,
		7,1,5,2,8,0,7,3,1,7,6,7,9,0,7,7,0,7,1,5,7,2,1,3,4,4,4,7,3,0,6,0,5,7,0,0,7,3,3,4,9,2,4,3,6,9,3,1,1,3,
		8,3,5,0,4,9,3,1,6,3,1,2,8,4,0,4,2,5,1,2,1,9,2,5,6,5,1,7,9,8,0,6,9,4,1,1,3,5,2,8,0,1,3,1,4,7,0,1,3,0,
		4,7,8,1,6,4,3,7,8,8,5,1,8,5,2,9,0,9,2,8,5,4,5,2,0,1,1,6,5,8,3,9,3,4,1,9,6,5,6,2,1,3,4,9,1,4,3,4,1,5,
		9,5,6,2,5,8,6,5,8,6,5,5,7,0,5,5,2,6,9,0,4,9,6,5,2,0,9,8,5,8,0,3,3,8,5,0,7,2,2,4,2,6,4,8,2,9,3,9,7,2,
		8,5,8,4,7,8,3,1,6,3,0,5,7,7,7,7,5,6,0,6,8,8,8,7,6,4,4,6,2,4,8,2,4,6,8,5,7,9,2,6,0,3,9,5,3,5,2,7,7,3,
		4,8,0,3,0,4,8,0,2,9,0,0,5,8,7,6,0,7,5,8,2,5,1,0,4,7,4,7,0,9,1,6,4,3,9,6,1,3,6,2,6,7,6,0,4,4,9,2,5,6,
		2,7,4,2,0,4,2,0,8,3,2,0,8,5,6,6,1,1,9,0,6,2,5,4,5,4,3,3,7,2,1,3,1,5,3,5,9,5,8,4,5,0,6,8,7,7,2,4,6,0,
		2,9,0,1,6,1,8,7,6,6,7,9,5,2,4,0,6,1,6,3,4,2,5,2,2,5,7,7,1,9,5,4,2,9,1,6,2,9,9,1,9,3,0,6,4,5,5,3,7,7,
		9,9,1,4,0,3,7,3,4,0,4,3,2,8,7,5,2,6,2,8,8,8,9,6,3,9,9,5,8,7,9,4,7,5,7,2,9,1,7,4,6,4,2,6,3,5,7,4,5,5,
		2,5,4,0,7,9,0,9,1,4,5,1,3,5,7,1,1,1,3,6,9,4,1,0,9,1,1,9,3,9,3,2,5,1,9,1,0,7,6,0,2,0,8,2,5,2,0,2,6,1,
		8,7,9,8,5,3,1,8,8,7,7,0,5,8,4,2,9,7,2,5,9,1,6,7,7,8,1,3,1,4,9,6,9,9,0,0,9,0,1,9,2,1,1,6,9,7,1,7,3,7,
		2,7,8,4,7,6,8,4,7,2,6,8,6,0,8,4,9,0,0,3,3,7,7,0,2,4,2,4,2,9,1,6,5,1,3,0,0,5,0,0,5,1,6,8,3,2,3,3,6,4,
		3,5,0,3,8,9,5,1,7,0,2,9,8,9,3,9,2,2,3,3,4,5,1,7,2,2,0,1,3,8,1,2,8,0,6,9,6,5,0,1,1,7,8,4,4,0,8,7,4,5,
		1,9,6,0,1,2,1,2,2,8,5,9,9,3,7,1,6,2,3,1,3,0,1,7,1,1,4,4,4,8,4,6,4,0,9,0,3,8,9,0,6,4,4,9,5,4,4,4,0,0,
		6,1,9,8,6,9,0,7,5,4,8,5,1,6,0,2,6,3,2,7,5,0,5,2,9,8,3,4,9,1,8,7,4,0,7,8,6,6,8,0,8,8,1,8,3,3,8,5,1,0,
		2,2,8,3,3,4,5,0,8,5,0,4,8,6,0,8,2,5,0,3,9,3,0,2,1,3,3,2,1,9,7,1,5,5,1,8,4,3,0,6,3,5,4,5,5,0,0,7,6,6,
		8,2,8,2,9,4,9,3,0,4,1,3,7,7,6,5,5,2,7,9,3,9,7,5,1,7,5,4,6,1,3,9,5,3,9,8,4,6,8,3,3,9,3,6,3,8,3,0,4,7,
		4,6,1,1,9,9,6,6,5,3,8,5,8,1,5,3,8,4,2,0,5,6,8,5,3,3,8,6,2,1,8,6,7,2,5,2,3,3,4,0,2,8,3,0,8,7,1,1,2,3,
		2,8,2,7,8,9,2,1,2,5,0,7,7,1,2,6,2,9,4,6,3,2,2,9,5,6,3,9,8,9,8,9,8,9,3,5,8,2,1,1,6,7,4,5,6,2,7,0,1,0,
		2,1,8,3,5,6,4,6,2,2,0,1,3,4,9,6,7,1,5,1,8,8,1,9,0,9,7,3,0,3,8,1,1,9,8,0,0,4,9,7,3,4,0,7,2,3,9,6,1,0,
		3,6,8,5,4,0,6,6,4,3,1,9,3,9,5,0,9,7,9,0,1,9,0,6,9,9,6,3,9,5,5,2,4,5,3,0,0,5,4,5,0,5,8,0,6,8,5,5,0,1,
		9,5,6,7,3,0,2,2,9,2,1,9,1,3,9,3,3,9,1,8,5,6,8,0,3,4,4,9,0,3,9,8,2,0,5,9,5,5,1,0,0,2,2,6,3,5,3,5,3,6,
		1,9,2,0,4,1,9,9,4,7,4,5,5,3,8,5,9,3,8,1,0,2,3,4,3,9,5,5,4,4,9,5,9,7,7,8,3,7,7,9,0,2,3,7,4,2,1,6,1,7,
		2,7,1,1,1,7,2,3,6,4,3,4,3,5,4,3,9,4,7,8,2,2,1,8,1,8,5,2,8,6,2,4,0,8,5,1,4,0,0,6,6,6,0,4,4,3,3,2,5,8,
		8,8,5,6,9,8,6,7,0,5,4,3,1,5,4,7,0,6,9,6,5,7,4,7,4,5,8,5,5,0,3,3,2,3,2,3,3,4,2,1,0,7,3,0,1,5,4,5,9,4,
		0,5,1,6,5,5,3,7,9,0,6,8,6,6,2,7,3,3,3,7,9,9,5,8,5,1,1,5,6,2,5,7,8,4,3,2,2,9,8,8,2,7,3,7,2,3,1,9,8,9,
		8,7,5,7,1,4,1,5,9,5,7,8,1,1,1,9,6,3,5,8,3,3,0,0,5,9,4,0,8,7,3,0,6,8,1,2,1,6,0,2,8,7,6,4,9,6,2,8,6,7,
		4,4,6,0,4,7,7,4,6,4,9,1,5,9,9,5,0,5,4,9,7,3,7,4,2,5,6,2,6,9,0,1,0,4,9,0,3,7,7,8,1,9,8,6,8,3,5,9,3,8,
		1,4,6,5,7,4,1,2,6,8,0,4,9,2,5,6,4,8,7,9,8,5,5,6,1,4,5,3,7,2,3,4,7,8,6,7,3,3,0,3,9,0,4,6,8,8,3,8,3,4,
		3,6,3,4,6,5,5,3,7,9,4,9,8,6,4,1,9,2,7,0,5,6,3,8,7,2,9,3,1,7,4,8,7,2,3,3,2,0,8,3,7,6,0,1,1,2,3,0,2,9,
		9,1,1,3,6,7,9,3,8,6,2,7,0,8,9,4,3,8,7,9,9,3,6,2,0,1,6,2,9,5,1,5,4,1,3,3,7,1,4,2,4,8,9,2,8,3,0,7,2,2,
		0,1,2,6,9,0,1,4,7,5,4,6,6,8,4,7,6,5,3,5,7,6,1,6,4,7,7,3,7,9,4,6,7,5,2,0,0,4,9,0,7,5,7,1,5,5,5,2,7,8,
		1,9,6,5,3,6,2,1,3,2,3,9,2,6,4,0,6,1,6,0,1,3,6,3,5,8,1,5,5,9,0,7,4,2,2,0,2,0,2,0,3,1,8,7,2,7,7,6,0,5,
		2,7,7,2,1,9,0,0,5,5,6,1,4,8,4,2,5,5,5,1,8,7,9,2,5,3,0,3,4,3,5,1,3,9,8,4,4,2,5,3,2,2,3,4,1,5,7,6,2,3,
		3,6,1,0,6,4,2,5,0,6,3,9,0,4,9,7,5,0,0,8,6,5,6,2,7,1,0,9,5,3,5,9,1,9,4,6,5,8,9,7,5,1,4,1,3,1,0,3,4,8,
		2,2,7,6,9,3,0,6,2,4,7,4,3,5,3,6,3,2,5,6,9,1,6,0,7,8,1,5,4,7,8,1,8,1,1,5,2,8,4,3,6,6,7,9,5,7,0,6,1,1,
		0,8,6,1,5,3,3,1,5,0,4,4,5,2,1,2,7,4,7,3,9,2,4,5,4,4,9,4,5,4,2,3,6,8,2,8,8,6,0,6,1,3,4,0,8,4,1,4,8,6,
		3,7,7,6,7,0,0,9,6,1,2,0,7,1,5,1,2,4,9,1,4,0,4,3,0,2,7,2,5,3,8,6,0,7,6,4,8,2,3,6,3,4,1,4,3,3,4,6,2,3,
		5,1,8,9,7,5,7,6,6,4,5,2,1,6,4,1,3,7,6,7,9,6,9,0,3,1,4,9,5,0,1,9,1,0,8,5,7,5,9,8,4,4,2,3,9,1,9,8,6,2,
		9,1,6,4,2,1,9,3,9,9,4,9,0,7,2,3,6,2,3,4,6,4,6,8,4,4,1,1,7,3,9,4,0,3,2,6,5,9,1,8,4,0,4,4,3,7,8,0,5,1,
		3,3,3,8,9,4,5,2,5,7,4,2,3,9,9,5,0,8,2,9,6,5,9,1,2,2,8,5,0,8,5,5,5,8,2,1,5,7,2,5,0,3,1,0,7,1,2,5,7,0,
		1,2,6,6,8,3,0,2,4,0,2,9,2,9,5,2,5,2,2,0,1,1,8,7,2,6,7,6,7,5,6,2,2,0,4,1,5,4,2,0,5,1,6,1,8,4,1,6,3,4,
		8,4,7,5,6,5,1,6,9,9,9,8,1,1,6,1,4,1,0,1,0,0,2,9,9,6,0,7,8,3,8,6,9,0,9,2,9,1,6,0,3,0,2,8,8,4,0,0,2,6,
		9,1,0,4,1,4,0,7,9,2,8,8,6,2,1,5,0,7,8,4,2,4,5,1,6,7,0,9,0,8,7,0,0,0,6,9,9,2,8,2,1,2,0,6,6,0,4,1,8,3,
		7,1,8,0,6,5,3,5,5,6,7,2,5,2,5,3,2,5,6,7,5,3,2,8,6,1,2,9,1,0,4,2,4,8,7,7,6,1,8,2,5,8,2,9,7,6,5,1,5,7,
		9,5,9,8,4,7,0,3,5,6,2,2,2,6,2,9,3,4,8,6,0,0,3,4,1,5,8,7,2,2,9,8,0,5,3,4,9,8,9,6,5,0,2,2,6,2,9,1,7,4,
		8,7,8,8,2,0,2,7,3,4,2,0,9,2,2,2,2,4,5,3,3,9,8,5,6,2,6,4,7,6,6,9,1,4,9,0,5,5,6,2,8,4,2,5,0,3,9,1,2,7,
		5,7,7,1,0,2,8,4,0,2,7,9,9,8,0,6,6,3,6,5,8,2,5,4,8,8,9,2,6,4,8,8,0,2,5,4,5,6,6,1,0,1,7,2,9,6,7,0,2,6,
		6,4,0,7,6,5,5,9,0,4,2,9,0,9,9,4,5,6,8,1,5,0,6,5,2,6,5,3,0,5,3,7,1,8,2,9,4,1,2,7,0,3,3,6,9,3,1,3,7,8,
		5,1,7,8,6,0,9,0,4,0,7,0,8,6,6,7,1,1,4,9,6,5,5,8,3,4,3,4,3,4,7,6,9,3,3,8,5,7,8,1,7,1,1,3,8,6,4,5,5,8,
		7,3,6,7,8,1,2,3,0,1,4,5,8,7,6,8,7,1,2,6,6,0,3,4,8,9,1,3,9,0,9,5,6,2,0,0,9,9,3,9,3,6,1,0,3,1,0,2,9,1,
		6,1,6,1,5,2,8,8,1,3,8,4,3,7,9,0,9,9,0,4,2,3,1,7,4,7,3,3,6,3,9,4,8,0,4,5,7,5,9,3,1,4,9,3,1,4,0,5,2,9,
		7,6,3,4,7,5,7,4,8,1,1,9,3,5,6,7,0,9,1,1,0,1,3,7,7,5,1,7,2,1,0,0,8,0,3,1,5,5,9,0,2,4,8,5,3,0,9,0,6,6,
		9,2,0,3,7,6,7,1,9,2,2,0,3,3,2,2,9,0,9,4,3,3,4,6,7,6,8,5,1,4,2,2,1,4,4,7,7,3,7,9,3,9,3,7,5,1,7,0,3,4,
		4,3,6,6,1,9,9,1,0,4,0,3,3,7,5,1,1,1,7,3,5,4,7,1,9,1,8,5,5,0,4,6,4,4,9,0,2,6,3,6,5,5,1,2,8,1,6,2,2,8,
		8,2,4,4,6,2,5,7,5,9,1,6,3,3,3,0,3,9,1,0,7,2,2,5,3,8,3,7,4,2,1,8,2,1,4,0,8,8,3,5,0,8,6,5,7,3,9,1,7,7,
		1,5,0,9,6,8,2,8,8,7,4,7,8,2,6,5,6,9,9,5,9,9,5,7,4,4,9,0,6,6,1,7,5,8,3,4,4,1,3,7,5,2,2,3,9,7,0,9,6,8,
		3,4,0,8,0,0,5,3,5,5,9,8,4,9,1,7,5,4,1,7,3,8,1,8,8,3,9,9,9,4,4,6,9,7,4,8,6,7,6,2,6,5,5,1,6,5,8,2,7,6,
		5,8,4,8,3,5,8,8,4,5,3,1,4,2,7,7,5,6,8,7,9,0,0,2,9,0,9,5,1,7,0,2,8,3,5,2,9,7,1,6,3,4,4,5,6,2,1,2,9,6,
		4,0,4,3,5,2,3,1,1,7,6,0,0,6,6,5,1,0,1,2,4,1,2,0,0,6,5,9,7,5,5,8,5,1,2,7,6,1,7,8,5,8,3,8,2,9,2,0,4,1,
		9,7,4,8,4,4,2,3,6,0,8,0,0,7,1,9,3,0,4,5,7,6,1,8,9,3,2,3,4,9,2,2,9,2,7,9,6,5,0,1,9,8,7,5,1,8,7,2,1,2,
		7,2,6,7,5,0,7,9,8,1,2,5,5,4,7,0,9,5,8,9,0,4,5,5,6,3,5,7,9,2,1,2,2,1,0,3,3,3,4,6,6,9,7,4,9,9,2,3,5,6,
		3,0,2,5,4,9,4,7,8,0,2,4,9,0,1,1,4,1,9,5,2,1,2,3,8,2,8,1,5,3,0,9,1,1,4,0,7,9,0,7,3,8,6,0,2,5,1,5,2,2,
		7,4,2,9,9,5,8,1,8,0,7,2,4,7,1,6,2,5,9,1,6,6,8,5,4,5,1,3,3,3,1,2,3,9,4,8,0,4,9,4,7,0,7,9,1,1,9,1,5,3,
		2,6,7,3,4,3,0,2,8,2,4,4,1,8,6,0,4,1,4,2,6,3,6,3,9,5,4,8,0,0,0,4,4,8,0,0,2,6,7,0,4,9,6,2,4,8,2,0,1,7,
		9,2,8,9,6,4,7,6,6,9,7,5,8,3,1,8,3,2,7,1,3,1,4,2,5,1,7,0,2,9,6,9,2,3,4,8,8,9,6,2,7,6,6,8,4,4,0,3,2,3,
		2,6,0,9,2,7,5,2,4,9,6,0,3,5,7,9,9,6,4,6,9,2,5,6,5,0,4,9,3,6,8,1,8,3,6,0,9,0,0,3,2,3,8,0,9,2,9,3,4,5,
		9,5,8,8,9,7,0,6,9,5,3,6,5,3,4,9,4,0,6,0,3,4,0,2,1,6,6,5,4,4,3,7,5,5,8,9,0,0,4,5,6,3,2,8,8,2,2,5,0,5,
		4,5,2,5,5,6,4,0,5,6,4,4,8,2,4,6,5,1,5,1,8,7,5,4,7,1,1,9,6,2,1,8,4,4,3,9,6,5,8,2,5,3,3,7,5,4,3,8,8,5,
		6,9,0,9,4,1,1,3,0,3,1,5,0,9,5,2,6,1,7,9,3,7,8,0,0,2,9,7,4,1,2,0,7,6,6,5,1,4,7,9,3,9,4,2,5,9,0,2,9,8,
		9,6,9,5,9,4,6,9,9,5,5,6,5,7,6,1,2,1,8,6,5,6,1,9,6,7,3,3,7,8,6,2,3,6,2,5,6,1,2,5,2,1,6,3,2,0,8,6,2,8,
		6,9,2,2,2,1,0,3,2,7,4,8,8,9,2,1,8,6,5,4,3,6,4,8,0,2,2,9,6,7,8,0,7,0,5,7,6,5,6,1,5,1,4,4,6,3,2,0,4,6,
		9,2,7,9,0,6,8,2,1,2,0,7,3,8,8,3,7,7,8,1,4,2,3,3,5,6,2,8,2,3,6,0,8,9,6,3,2,0,8,0,6,8,2,2,2,4,6,8,0,1,
		2,2,4,8,2,6,1,1,7,7,1,8,5,8,9,6,3,8,1,4,0,9,1,8,3,9,0,3,6,7,3,6,7,2,2,2,0,8,8,8,3,2,1,5,1,3,7,5,5,6,
		0,0,3,7,2,7,9,8,3,9,4,0,0,4,1,5,2,9,7,0,0,2,8,7,8,3,0,7,6,6,7,0,9,4,4,4,7,4,5,6,0,1,3,4,5,5,6,4,1,7,
		2,5,4,3,7,0,9,0,6,9,7,9,3,9,6,1,2,2,5,7,1,4,2,9,8,9,4,6,7,1,5,4,3,5,7,8,4,6,8,7,8,8,6,1,4,4,4,5,8,1,
		2,3,1,4,5,9,3,5,7,1,9,8,4,9,2,2,5,2,8,4,7,1,6,0,5,0,4,9,2,2,1,2,4,2,4,7,0,1,4,1,2,1,4,7,8,0,5,7,3,4,
		5,5,1,0,5,0,0,8,0,1,9,0,8,6,9,9,6,0,3,3,0,2,7,6,3,4,7,8,7,0,8,1,0,8,1,7,5,4,5,0,1,1,9,3,0,7,1,4,1,2,
		2,3,3,9,0,8,6,6,3,9,3,8,3,3,9,5,2,9,4,2,5,7,8,6,9,0,5,0,7,6,4,3,1,0,0,6,3,8,3,5,1,9,8,3,4,3,8,9,3,4,
		1,5,9,6,1,3,1,8,5,4,3,4,7,5,4,6,4,9,5,5,6,9,7,8,1,0,3,8,2,9,3,0,9,7,1,6,4,6,5,1,4,3,8,4,0,7,0,0,7,0,
		7,3,6,0,4,1,1,2,3,7,3,5,9,9,8,4,3,4,5,2,2,5,1,6,1,0,5,0,7,0,2,7,0,5,6,2,3,5,2,6,6,0,1,2,7,6,4,8,4,8,
		3,0,8,4,0,7,6,1,1,8,3,0,1,3,0,5,2,7,9,3,2,0,5,4,2,7,4,6,2,8,6,5,4,0,3,6,0,3,6,7,4,5,3,2,8,6,5,1,0,5,
		7,0,6,5,8,7,4,8,8,2,2,5,6,9,8,1,5,7,9,3,6,7,8,9,7,6,6,9,7,4,2,2,0,5,7,5,0,5,9,6,8,3,4,4,0,8,6,9,7,3,
		5,0,2,0,1,4,1,0,2,0,6,7,2,3,5,8,5,0,2,0,0,7,2,4,5,2,2,5,6,3,2,6,5,1,3,4,1,0,5,5,9,2,4,0,1,9,0,2,7,4,
		2,1,6,2,4,8,4,3,9,1,4,0,3,5,9,9,8,9,5,3,5,3,9,4,5,9,0,9,4,4,0,7,0,4,6,9,1,2,0,9,1,4,0,9,3,8,7,0,0,1,
		2,6,4,5,6,0,0,1,6,2,3,7,4,2,8,8,0,2,1,0,9,2,7,6,4,5,7,9,3,1,0,6,5,7,9,2,2,9,5,5,2,4,9,8,8,7,2,7,5,8,
		4,6,1,0,1,2,6,4,8,3,6,9,9,9,8,9,2,2,5,6,9,5,9,6,8,8,1,5,9,2,0,5,6,0,0,1,0,1,6,5,5,2,5,6,3,7,5,6,8,
			};


}
